I've just looked inside my cajon - professionally built, don't know the make. Peering through the sound hole, I can see a 10" length of drum snare held onto the striking face of the box in a vertical orientation by metal clips at the ends. The snare is positioned in the bottom LH corner of the cajon. I can see a small wooden block pressing a foam strip onto the snare, held in place by a length of elastic stretched between the metal end-clips. Clearly, the idea is that the small block can be slid along the snare wire to change the tone. No idea how you actually reach it, though! I've attempted to photograph it.
On a seperate note, I found it very uncomfortable sitting on top of the box and leaning forward. This playing position really hurt my back. So, I knocked together a folding stand that enables me to play while sitting on a comfy chair, with the striking face of the cajon at an angle between my legs. See photo.